I am a high school physics intern, trying to figure out how calorimeter accuracy affects the recoiled proton's mass in a collision, where an electron beam is aimed at a proton target. The electron beam emits a virtual photon and scatters off one of the virtual pions around the proton, and the pion becomes real due to the virtual photon energy and flies off to decay into two photons. The proton recoils. I am interested in calculating the mass of the recoiled proton. (should be the same as the initial proton, but I want it to vary based on detected quantities of the angle, momentum, energy of the pion, so I can build a Gaussian distribution of the proton' mass, affected by m,p, and angle of pion) I know the proton momentum quantity, but am searching for a different equation for the proton energy to find recoiled proton mass through proton' mass= SQRT(Ep^2-Pp^2) because the one that I have for proton energy (laboratory): Ep=SQRT(Pp^2+Mp) makes it so that the proton' mass will always be 0.94 GeV because that is what I input in this equation (kind of a circular function) I've tried Ep=(nu+Mp)-Epi, where Epi is energy of pion and nu is energy of the virtual photon..but am not sure if it is correct. Can someone suggest other ways to calculate energy of the recoiled proton? I've also tried Ep=W-Epi...but I need Ep in laboratory frame and W, center of mass energy, is in center of mass frame....so it doesn't really work. Thank you so much!